I ran some statistical analysis on your dataset. As your article points out, TTFB is very important. The p-value (chance of the correlation coming from random noise) is less than 0.1%.

"Full Render Time" is also statistically significant - either alone or in combination with TTFB. What's surprising is FRT has a negative coefficient. As pages render quicker, they show up in worse search rankings.

I like your theory that Google's spider finds it easier to calculate TTFB. But this only explains Full Render having no correlation - not a negative correlation.

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I'm seeing similar issues in my roughly analogous work (connecting speed to customer value). For me, the confounding factors can be pretty rough - a lot of work is needed to remove them.

Seems like your confounding factors (maybe the most relevant sites have more content?) are big enough to swamp the important effect you're tracking. The only speed factor that runs in the same direction as "popular sites with rich content" is TTFB.

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Suggestion for a followup article

I'm sure this analysis required a ton of effort. Hopefully, the traffic was enough to justify the cost for another look.

Maybe repeat the same analysis in a month to see if any ranks and speeds changed for individual sites? The inbound link count is unlikely to be greatly changed, but some sites may have caught the Web Page Optimization fever. If so, you might be able to look at these sites alone and remove some of the confounding factors. You can reduce the noise by pulling multiple pagespeed samples for each site.